Adiabatic perturbation theory: From landau-zener problem to quenching through a quantum critical point

Abstract

Dynamics in closed systems recently attracted a lot of theoretical interest largely following experimental developments in cold atom systems (see e.g., [1] for a review). Several spectacular experiments already explored different aspects of non-equilibrium dynamics in interacting many-particle systems [2-8]. Recent theoretical works in this context focused on various topics, for instance: connection of dynamics and thermodynamics [9-11 M. Rigol, unpublished], dynamics following a sudden quench Sudden quench in low dimensional systems [11-23, L. Mathey and A. Polkovnikov, unpublished; A. Iucci and M.A. Cazalilla,unpublished], adiabatic dynamics near quantum critical points [24-37, D. Chowdhury et al., unpublished; K. Sengupta and D. Sen, unpublished; A.P. Itin and P. Törmä, unpublished; F. Pollmann et al., unpublished] Critical point!quantum and others. Though there is still very limited understanding of the generic aspects of non-equilibrium quantum dynamics, it has been recognized that such issues as integrability, dimensionality, universality (near critical points) can be explored to understand the non-equilibrium behavior of many-particle systems in various specific situations. © 2010 Springer-Verlag Berlin Heidelberg.